Inverters use some power even when nothing is plugged into the AC sockets. I would think that the power switch on the front would shut the electronics down, but it may not. Try shutting off the breaker for that circuit rather than relying on units power switch.

I think you mean 2000 watts, not amps. Still a pretty big unit. That's almost 200 amps DC at full load, Hope you have a big house bank.

Hmmmm, when googling I found this:Powershield Commander 2000 VA Line Interactive, Sine Wave UPS
More a UPS than an inverter (2000VA/1600 watts). It looks that this type has an built-in battery, one that will last for 30 minutes or so.
The specifications does not show a drain current when not connected to a load. but if no other batteries are connected, I guess indeed your small internal battery will be flat very soon!!!
Inverters of this kind of power can use 8 to 18 Watt for power when not 'used'.